What is the derivative of arctan(ax) ?

The derivative of arctan(ax) is a/(a^2x^2+1)

What is the first derivative of arctan(ax) ?

The first derivative of arctan(ax) is a/(a^2x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arctan (a x))

\frac{a}{a ^{2} x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (a x))

Apply the chain rule:

\frac{1}{( a x ) ^{2} + 1} \frac{d}{d x} (a x)

= \frac{1}{( a x ) ^{2} + 1} \frac{d}{d x} (a x)

\frac{d}{d x} (a x) = a

= \frac{1}{( a x ) ^{2} + 1} a

Simplify

\frac{1}{( a x ) ^{2} + 1} a : \frac{a}{a ^{2} x ^{2} + 1}

= \frac{a}{a ^{2} x ^{2} + 1}

What is the derivative of arctan(ax) ?
The derivative of arctan(ax) is a/(a^2x^2+1)
What is the first derivative of arctan(ax) ?
The first derivative of arctan(ax) is a/(a^2x^2+1)